1. The problem statement, all variables and given/known data The one-dimensional heat diffusion equation is given by : ∂t(x,t)/∂t = α[∂^2T(x,t) / ∂x^2] where α is positive. Is the following a possible solution? Assume that the constants a and b can take any positive value. T(x,t) = exp(at)cos(bx) 2. Relevant equations 3. The attempt at a solution T(x,t) = exp(at)cos(bx) ∂T/∂t = a exp(at) cos(bx) ∂^2 T/∂x^2 = -b^2 exp(at) cos(bx) As a, b and α are all positive this cannot be a solution. A friend and I were working on this and got the answer above. Though as it was about a week ago I can't exactly remember what we've done here. In the first step I think we've differentiated exp(at) with respect to t, treating the cos(bx) as a constant multiplier, which become a exp(at) cos(bx). Is that all correct above? Then we differentiated again with respect to t. So wouldn't that become; ∂^2 T/∂x^2 = a^2 exp(at) cos(bx) Why did we previously get ∂^2 T/∂x^2 = -b^2 exp(at) cos(bx) Thanks!